ZapperZ said:
Woo hoo! Someone finally referenced the thread I started on this earlier!
Which I was about to do myself. True, the wording of the title was a bit different, but I feel I was essentially asking the same question as the OP here.
Actually I kept thinking about that thread and I think it cleared things up for me quite a bit.
Here's my take on force and Newton's laws:
The purpose of classical mechanics is to account for the 'complicated' motion of bodies (rocks, arrows, cars, planets...). Intuitively we recognise that an object's 'complicated motion' arises from the influence of other objects upon it. 'Force' is our special word, for the influence that a body has on another body's motion.
The ancients thought that 'uncomplicated' motion was rest, and therefore non-rest needed explaining, in terms of the influence of other bodies. Newton said that actually 'uncomplicated motion' was uniform-velocity, and it is
changes in velocity that arise from the influence of other objects. That's the basic content of Newton's FIRST Law (not second): to define force as 'that influence from one body, which changes another body's velocity'. (regarding different frames of reference, I presume the physical content of N1 is to assert that
there are frames of reference in which it is true, and then we can do maths later to worry about the frames of reference in which it is not true)
Newton's Second law then elaborates. To me it actually contains several statements about the way nature works... there's a lot of subtle points hidden in 'F=ma'.
Firstly, it notices that different bodies are accelerated differently by the same forces acting on them - some accelerate more, some less. So N2 states that each body has a quantity called '(inertial) mass', such that the acceleration a body experiences for a given force is inversely proportional to its mass.
Secondly it asserts (or maybe just
requires) that that mass is the same for all situations that the body might find itself in, and that the mass is constant over time. If the mass appears to change, it is because the body has broken up, or stuck to something else, such that the masses of bodies 'add up' in the simple way.
Thirdly it asserts that when more than one force acts on a body, the forces add vectorially.
Well that's what I got out of the discussion anyway. I'm still turning over all those concepts in my mind.